Abstract: The mini-course is an introductory and self-contained approach to the method of intrinsic scaling, aiming at bringing to light what is really essential in this powerful tool in the analysis of degenerate and singular equations. The theory is presented from scratch for the simplest model case of the degenerate p-Laplace equation, leaving aside
technical renements needed to deal with more general situations. A striking feature of the method is its pervasiveness in terms of the applications and I hope to convince the audience of its strength as a systematic approach to regularity for an important and relevant class of nonlinear partial dierential equations. I will extensively follow my book
$$extract_itex$$14$$/extract_itex$$ , with complements and extensions from a variety of sources (listed in the references), mainly
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Lecture I.
An impressionist history lesson: from Hilbert's 19th problem to DeGiorgi-Nash-Moser theory; the quasilinear case { contributions from the Russian school; enters DiBenedetto { the method of intrinsic scaling.

Lecture II.
The building blocks of the theory: local energy and logarithmic estimates. The geometric setting and an alternative.

Lecture III.
The rst alternative: getting started; expansion in time and the role of the logarithmic estimates; reduction of the oscillation.

Lecture IV.
Towards the Holder continuity: the second alternative; the recursive argument.

Lecture V.
The singular case and further generalisations: immiscible uids and chemotaxis; phase transitions.
제목
2016-05-17  14:00-17:00  Fully Nonlinear Elliptic Equations Lihe Wang  129-406
2016-05-18  14:00-17:00  Regualarity Theory for Elliptic and Parabolic Equations Lihe Wang  129-406
2017-01-05  10:00-12:00  Regularity theory for elliptic equations Lihe Wang  27-325
2017-01-05  16:00-18:00  Regularity theory for parabolic equations Lihe Wang  27-325
2017-04-20  16:00-18:00  편미분방정식 초청강연 Lihe Wang  129-301
2018-05-21  15:00-16:00  Liouville type theorems in cylinders Lihe Wang  129-301
2019-06-20  15:00-18:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116
2019-06-21  10:00-12:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116
2019-06-19  17:00-18:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116
2019-06-20  10:00-12:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116
2019-06-21  14:00-16:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116
2018-01-25  10:00-12:00  Regularity of subelliptic equations Lihe Wang  27-325
2022-12-21  14:00-16:00  Fully nonlinear elliptic euqations Lihe Wang  27-325
2022-12-22  14:00-16:00  Fully nonlinear parabolic equations Lihe Wang  27-325
2021-11-05  10:00-12:00  Regularity of elliptic partial differential equations 1 Lihe Wang  선택
2021-11-12  10:00-12:00  Analysis for Elliptic Equations 2 Lihe Wang  선택
2021-11-19  10:00-12:00  Analysis for Elliptic Equations #3 Lihe Wang  선택
2021-12-03  10:00-12:00  Analysis for Elliptic Equations #4 Lihe Wang  선택
2019-01-23  16:00-17:00  Regularity for elliptic equations in heterogeneous media Li-Ming Yeh  129-301
2014-04-07  14:00-15:00  Dfferential Games of Evasion and Pontryagin\'s Lemma Lev Yugay  129-307